Soliton solutions of the fermion-Skyrmion system in (2+1) dimensions

TL;DR

This paper investigates how fermionic modes interact with baby Skyrmions in (2+1) dimensions, revealing a single fermionic level that shifts with coupling strength and significantly deforms the Skyrmion at strong coupling.

Contribution

It demonstrates the backreaction effects of fermionic modes on baby Skyrmions and characterizes the fermionic spectrum and deformation behavior at varying coupling strengths.

Findings

Existence of a fermionic tower localized by the Skyrmion

Single fermionic level flows from positive to negative with increasing coupling

Strong coupling deforms the Skyrmion, creating regions of negative topological charge density

Abstract

We study effects of backreaction of the fermionic modes localized by the baby Skyrmion in the (2+1)-dimensional Skyrme model. It is shown that there is a tower of fermionic modes of two different types, localized by the soliton, however there is only one fermionic level, which flows from positive to negative value as coupling increases. Considering the strong coupling regime we observe that the coupling of the bosonic field to the fermions may strongly deform the Skyrmion, in particular the regions of negative topological charge density appear.